Complex Numbers: What's My Rule? – Discover the Hidden Transformation

This GeoGebra activity presents an interactive exploration of complex numbers on the complex plane. Points A, B, and C represent complex numbers; users can drag A and B, and point C responds dynamically. The challenge is to deduce the mathematical rule that defines C from its movement. The core concepts involve geometric representation of complex numbers, complex operations (addition, multiplication, conjugation, modulus), and transformations such as rotation, scaling, or reflection. The construction uses GeoGebra commands including Intersect, Circle, and Mirror, with objects A, C_1, B, D, c, and C, suggesting that C may be defined as an intersection of a circle and a line, or as a mirror image of another point. This resource is ideal for high school or early college students learning complex numbers, promoting inquiry-based discovery of how algebraic rules manifest geometrically, and strengthening skills in pattern recognition, hypothesis testing, and mathematical reasoning.